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dlasdq.f(3)				      LAPACK				      dlasdq.f(3)

NAME
       dlasdq.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlasdq (UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU, C, LDC, WORK,
	   INFO)
	   DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal
	   e. Used by sbdsdc.

Function/Subroutine Documentation
   subroutine dlasdq (characterUPLO, integerSQRE, integerN, integerNCVT, integerNRU, integerNCC,
       double precision, dimension( * )D, double precision, dimension( * )E, double precision,
       dimension( ldvt, * )VT, integerLDVT, double precision, dimension( ldu, * )U, integerLDU,
       double precision, dimension( ldc, * )C, integerLDC, double precision, dimension( * )WORK,
       integerINFO)
       DLASDQ computes the SVD of a real bidiagonal matrix with diagonal d and off-diagonal e.
       Used by sbdsdc.

       Purpose:

	    DLASDQ computes the singular value decomposition (SVD) of a real
	    (upper or lower) bidiagonal matrix with diagonal D and offdiagonal
	    E, accumulating the transformations if desired. Letting B denote
	    the input bidiagonal matrix, the algorithm computes orthogonal
	    matrices Q and P such that B = Q * S * P**T (P**T denotes the transpose
	    of P). The singular values S are overwritten on D.

	    The input matrix U	is changed to U  * Q  if desired.
	    The input matrix VT is changed to P**T * VT if desired.
	    The input matrix C	is changed to Q**T * C	if desired.

	    See "Computing  Small Singular Values of Bidiagonal Matrices With
	    Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan,
	    LAPACK Working Note #3, for a detailed description of the algorithm.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		   On entry, UPLO specifies whether the input bidiagonal matrix
		   is upper or lower bidiagonal, and wether it is square are
		   not.
		      UPLO = 'U' or 'u'   B is upper bidiagonal.
		      UPLO = 'L' or 'l'   B is lower bidiagonal.

	   SQRE

		     SQRE is INTEGER
		   = 0: then the input matrix is N-by-N.
		   = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and
			(N+1)-by-N if UPLU = 'L'.

		   The bidiagonal matrix has
		   N = NL + NR + 1 rows and
		   M = N + SQRE >= N columns.

	   N

		     N is INTEGER
		   On entry, N specifies the number of rows and columns
		   in the matrix. N must be at least 0.

	   NCVT

		     NCVT is INTEGER
		   On entry, NCVT specifies the number of columns of
		   the matrix VT. NCVT must be at least 0.

	   NRU

		     NRU is INTEGER
		   On entry, NRU specifies the number of rows of
		   the matrix U. NRU must be at least 0.

	   NCC

		     NCC is INTEGER
		   On entry, NCC specifies the number of columns of
		   the matrix C. NCC must be at least 0.

	   D

		     D is DOUBLE PRECISION array, dimension (N)
		   On entry, D contains the diagonal entries of the
		   bidiagonal matrix whose SVD is desired. On normal exit,
		   D contains the singular values in ascending order.

	   E

		     E is DOUBLE PRECISION array.
		   dimension is (N-1) if SQRE = 0 and N if SQRE = 1.
		   On entry, the entries of E contain the offdiagonal entries
		   of the bidiagonal matrix whose SVD is desired. On normal
		   exit, E will contain 0. If the algorithm does not converge,
		   D and E will contain the diagonal and superdiagonal entries
		   of a bidiagonal matrix orthogonally equivalent to the one
		   given as input.

	   VT

		     VT is DOUBLE PRECISION array, dimension (LDVT, NCVT)
		   On entry, contains a matrix which on exit has been
		   premultiplied by P**T, dimension N-by-NCVT if SQRE = 0
		   and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).

	   LDVT

		     LDVT is INTEGER
		   On entry, LDVT specifies the leading dimension of VT as
		   declared in the calling (sub) program. LDVT must be at
		   least 1. If NCVT is nonzero LDVT must also be at least N.

	   U

		     U is DOUBLE PRECISION array, dimension (LDU, N)
		   On entry, contains a  matrix which on exit has been
		   postmultiplied by Q, dimension NRU-by-N if SQRE = 0
		   and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).

	   LDU

		     LDU is INTEGER
		   On entry, LDU  specifies the leading dimension of U as
		   declared in the calling (sub) program. LDU must be at
		   least max( 1, NRU ) .

	   C

		     C is DOUBLE PRECISION array, dimension (LDC, NCC)
		   On entry, contains an N-by-NCC matrix which on exit
		   has been premultiplied by Q**T  dimension N-by-NCC if SQRE = 0
		   and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).

	   LDC

		     LDC is INTEGER
		   On entry, LDC  specifies the leading dimension of C as
		   declared in the calling (sub) program. LDC must be at
		   least 1. If NCC is nonzero, LDC must also be at least N.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (4*N)
		   Workspace. Only referenced if one of NCVT, NRU, or NCC is
		   nonzero, and if N is at least 2.

	   INFO

		     INFO is INTEGER
		   On exit, a value of 0 indicates a successful exit.
		   If INFO < 0, argument number -INFO is illegal.
		   If INFO > 0, the algorithm did not converge, and INFO
		   specifies how many superdiagonals did not converge.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley,
	   USA

       Definition at line 211 of file dlasdq.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      dlasdq.f(3)
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